Global stability for a multi-group SVIR model with age of vaccination

In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investi- gated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.